Elementary Diagram

For a structure M in a language L, the elementary diagram is the set of all first-order L(M)-sentences (where L(M) is L expanded with a constant for each element of M) that are true in the expanded structure; it records every first-order fact about named elements of M.

Given a structure A, the elementary diagram Diag(A) is the set of all atomic and negated atomic sentences in the language expanded by naming each element a ∈ A with a new constant symbol c_a, that are true in A. It records complete atomic-level information about A with constants.